Question

A small commuter plane has 30 seats. The probability that any particular passenger will not show up for a flight is 0.10, independent of other passengers. The airline sells 32 tickets for the flight. The profit of each ticket is $1,000. The airline will reimburse 10,000 for each passenger who cannot enter the plane. Calculate the expected profit of each flight.

Answer 1

The total number of flight tickets sold = 32. For each ticket, the profit earned is 1000 dollars.

Hence, the profit for all tickets sold = 32*1000 = 32000 dollars.

Now, the airline will reimburse 10000 for each passenger who cannot enter the flight.

This can happen in two events.

1. When 31 passengers arrive, one passenger will be given 10000 dollars. The probability of a passenger arriving is 1-0.1 = 0.9.

Hence, the probability of 31 passengers arriving is

Hence, the amount that will be paid becomes:

2. When 32 passengers arrive, two passengers will be given 10000 dollars. Hence, the total reimbursement will be 20000. The probability of 32 passengers arriving is

Hence, the amount that will be paid becomes:

Hence, the expected profit becomes:

Therefore, for each flight the expected profit becomes 30,931.7 dollars.